| 1. |
- Abebaw, Tilahun, et al.
(författare)
-
Decomposition of D-modules over a hyperplane arrangement in the plane
- 2010
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 48:2, s. 211-229
-
Tidskriftsartikel (refereegranskat)abstract
- Let alpha(1), alpha(2),..., alpha(m) be linear forms defined on C-n and X = C-n\boolean OR(m)(i=1) V(alpha(i)), where V(alpha(i))={p is an element of C-n : alpha(i)(p)=0}. The coordinate ring O-X of X is a holonomic A(n)-module, where A(n) is the nth Weyl algebra and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a "" twisted"" variant of this An- module which is also holonomic. Define M-alpha(beta) to be the free rank-1 C[x](alpha)-module on the generator alpha(beta) (thought of as a multivalued function), where alpha(beta)=alpha(beta 1)(1),..., alpha(beta m)(m) and the multi-index beta=(beta(1),...,beta(m))is an element of C-m. Our main result is the computation of the number of decomposition factors of M-alpha(beta) and their description when n-2.
|
|
| 2. |
- Aghapournahr, Moharram, et al.
(författare)
-
Artinianness of local cohomology modules
- 2014
-
Ingår i: Arkiv för matematik. - : Royal Swedish Academy of Sciences, Institut Mittag-Leffler. - 0004-2080 .- 1871-2487. ; 52:1, s. 1-10
-
Tidskriftsartikel (refereegranskat)abstract
- Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about the artinianness of some special local cohomology modules in the graded case.
|
|
| 3. |
- Alexandersson, Per, 1987-, et al.
(författare)
-
Promotion and cyclic sieving on families of SSYT
- 2021
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 59:2, s. 247-274
-
Tidskriftsartikel (refereegranskat)abstract
- We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. The second family contains skew shapes, consisting of disjoint rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier results by B. Rhoades and later B. Fontaine and J. Kamnitzer. Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in the form of a bicyclic sieving phenomenon. One of the tools we use is a novel method for computing charge of skew semistandard tableaux, in the case when every number in the tableau occurs with the same frequency.
|
|
| 4. |
|
|
| 5. |
- Andersson, Mats, 1957
(författare)
-
A residue criterion for strong holomorphicity
- 2010
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 48:1, s. 1-15
-
Tidskriftsartikel (refereegranskat)abstract
- We give a local criterion in terms of a residue current for strong holomorphicity of a meromorphic function on an arbitrary pure-dimensional analytic variety. This generalizes a result by A. Tsikh for the case of a reduced complete intersection.
|
|
| 6. |
- Auscher, Pascal, et al.
(författare)
-
Solvability of elliptic systems with square integrable boundary data
- 2010
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 48:2, s. 253-287
-
Tidskriftsartikel (refereegranskat)abstract
- We consider second order elliptic divergence form systems with complex measurable coefficients A that are independent of the transversal coordinate, and prove that the set of A for which the boundary value problem with L-2 Dirichlet or Neumann data is well posed, is an open set. Furthermore we prove that these boundary value problems are well posed when A is either Hermitean, block or constant. Our methods apply to more general systems of partial differential equations and as an example we prove perturbation results for boundary value problems for differential forms.
|
|
| 7. |
- Bakas, Odysseas, et al.
(författare)
-
Notes on Hlog : structural properties, dyadic variants, and bilinear H1-BMO mappings
- 2022
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 60:2, s. 231-275
-
Tidskriftsartikel (refereegranskat)abstract
- This article is devoted to a study of the Hardy space Hlog(Rd) introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space H1 and a function in BMO to distributions that belong to Hlog based on dyadic paraproducts. We also point out analogues of classical results of Hardy–Littlewood, Zygmund, and Stein for Hlog and related Musielak–Orlicz spaces.
|
|
| 8. |
- Balletti, Gabriele, et al.
(författare)
-
Laplacian simplices associated to digraphs
- 2018
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 56:2, s. 243-264
-
Tidskriftsartikel (refereegranskat)abstract
- We associate to a finite digraph D a lattice polytope P-D whose vertices are the rows of the Laplacian matrix of D. This generalizes a construction introduced by Braun and the third author. As a consequence of the Matrix-Tree Theorem, we show that the normalized volume of P-D equals the complexity of D, and P-D contains the origin in its relative interior if and only if D is strongly connected. Interesting connections with other families of simplices are established and then used to describe reflexivity, the h*-polynomial, and the integer decomposition property of P-D in these cases. We extend Braun and Meyer's study of cycles by considering cycle digraphs. In this setting, we characterize reflexivity and show there are only four non-trivial reflexive Laplacian simplices having the integer decomposition property.
|
|
| 9. |
- Bazarganzadeh, Mahmoudreza, et al.
(författare)
-
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
- 2014
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 52:1, s. 21-42
-
Tidskriftsartikel (refereegranskat)abstract
- We study minimizers of the functional where B_{1}^{{\mathchoice {\raise .17ex\hbox {\scriptstyle +}} {\raise .17ex\hbox {\scriptstyle +}} {\raise .1ex\hbox {\scriptscriptstyle +}} {\scriptscriptstyle +}}}=\{x\in B_{1}: x_{1}>0\} , u=0 on {x∈B 1:x 1=0}, \lambda^{{\mathchoice {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .1ex\hbox {\scriptscriptstyle \pm }} {\scriptscriptstyle \pm }}} are two positive constants and 0<p<1. In two dimensions, we prove that the free boundary is a uniform C 1 graph up to the flat part of the fixed boundary and also that two-phase points cannot occur on this part of the fixed boundary. Here, the free boundary refers to the union of the boundaries of the sets {x:±u(x)>0}.
|
|
| 10. |
- Björklund, Johan, 1982-
(författare)
-
Encomplexed Brown Invariant of Real Algebraic Surfaces in RP3
- 2013
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 51:2, s. 251-267
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We construct an invariant of parametrized generic real algebraic surfaces in RP3 which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using the self intersection, which is a real algebraic curve with points of three local characters: the intersection of two real sheets, the intersection of two complex conjugate sheets or a Whitney umbrella. The Brown invariant was expressed through a self linking number of the self intersection by Kirby and Melvin. We extend the definition of this self linking number to the case of parametrized generic real algebraic surfaces.
|
|
| 11. |
- Borell, Stefan, et al.
(författare)
-
Embeddings through Discrete Sets of Discs
- 2008
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 46:2, s. 251-269
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate whether a Stein manifold M which allows proper holomorphic embedding into ℂ n can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of M is smaller than n/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.
|
|
| 12. |
- Brandes, Julia, et al.
(författare)
-
Two-dimensional Weyl sums failing square-root cancellation along lines
- 2023
-
Ingår i: Arkiv for Matematik. - 0004-2080 .- 1871-2487. ; 61:2, s. 267-276
-
Tidskriftsartikel (refereegranskat)abstract
- We show that a certain two-dimensional family of Weyl sums of length P takes values as large as P3/4+o(1) on almost all linear slices of the unit torus, contradicting a widely held expectation that Weyl sums should exhibit square-root cancellation on generic subvarieties of the unit torus. This is an extension of a result of J. Brandes, S. T. Parsell, C. Poulias, G. Shakan and R. C. Vaughan (2020) from quadratic and cubic monomials to general polynomials of arbitrary degree. The new ingredients of our approach are the classical results of E. Bombieri (1966) on exponential sums along a curve and R. J. Duffin and A. C. Schaeffer (1941) on Diophantine approximations by rational numbers with prime denominators.
|
|
| 13. |
- Dahlberg, Björn E. J.
(författare)
-
Total curvature and rearrangements.
- 2005
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 43:2, s. 323-345
-
Tidskriftsartikel (refereegranskat)abstract
- We study to what extent rearrangements preserve the integrability properties of higher order derivatives. It is well known that the second order derivatives of the rearrangement of a smooth function are not necessarily inL 1. We obtain a substitute for this fact. This is done by showing that the total curvature for the graph of the rearrangement of a function is bounded by the total curvature for the graph of the function itself.
|
|
| 14. |
- Deijfen, Maria, 1975-, et al.
(författare)
-
A preferential attachment model with random initial degrees
- 2009
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 47:1, s. 42-72
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, a random graph process{G(t)}t≥1 is studied and its degreesequence is analyzed. Let {Wt}t≥1 be an i.i.d. sequence. The graph process is defined so that ,at each integer time t, a new vertex with Wt edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on G(t−1), the probability that a given edge of vertex t is connected to vertex i is proportional to di (t−1)+δ, where di(t−1) is the degree of vertex i at time t−1, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent τ=min{τW, τP}, where τW is the power-law exponent of the initial degrees {Wt}t≥1 and τP the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.
|
|
| 15. |
- Deijfen, Maria, et al.
(författare)
-
Percolation in invariant Poisson graphs with i.i.d. degrees
- 2012
-
Ingår i: Arkiv for Matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 50:1, s. 41-58
-
Tidskriftsartikel (refereegranskat)abstract
- Let each point of a homogeneous Poisson process in R-d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme which is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components.
|
|
| 16. |
- Devroye, Luc, et al.
(författare)
-
Long and short paths in uniform random recursive dags
- 2011
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 49:1, s. 61-77
-
Tidskriftsartikel (refereegranskat)abstract
- In a uniform random recursive k-directed acyclic graph, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S (n) is the shortest path distance from node n to the root, then we determine the constant sigma such that S (n) /log n ->sigma in probability as n -> a. We also show that max (1a parts per thousand currency signia parts per thousand currency signn) S (i) /log n ->sigma in probability.
|
|
| 17. |
- Di Rocco, Sandra, et al.
(författare)
-
On surfaces in P-6 with no trisecant lines
- 2000
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 38:2, s. 231-261
-
Tidskriftsartikel (refereegranskat)abstract
- Examples of surfaces in P-6 with no trisecant lines are constructed. A partial classification recovering them is given and conjectured to be the complete one.
|
|
| 18. |
|
|
| 19. |
- Edlund, Tomas, et al.
(författare)
-
The pluripolar hull of a graph and fine analytic continuation
- 2006
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 44:1, s. 39-60
-
Tidskriftsartikel (refereegranskat)abstract
- We show that if the graph of an analytic function in the unit disk D is not complete pluripolar in C-2 then the projection of its pluripolar hull contains a fine neighborhood of a point p is an element of partial derivative D. Moreover the projection of the pluripolar hull is always finely open. On the other hand we show that if an analytic function f in D extends to a function T which is defined on a fine neighborhood of a point p is an element of partial derivative D and is finely analytic at p then the pluripolar hull of the graph of f contains the graph of F over a smaller fine neighborhood of p. We give several examples of functions with this property of fine analytic continuation. As a corollary we obtain new classes of analytic functions in the disk which have non-trivial pluripolar hulls, among them C-infinity functions on the closed unit disk which are nowhere analytically extendible and have infinitely-sheeted pluripolar hulls. Previous examples of functions with non-trivial pluripolar hull of the graph have fine analytic continuation.
|
|
| 20. |
- Eilertsen, S
(författare)
-
On weighted positivity and the Wiener regularity of a boundary point for the fractional Laplacian
- 2000
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 38:1, s. 53-75
-
Tidskriftsartikel (refereegranskat)abstract
- A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (-Delta)(mu) in R-n, ngreater than or equal to1, is obtained, for muis an element of(0, 1/2n)\(1, 1/2n-1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev. As in the polyharmonic case, the proof is based on a weighted positivity property of (-Delta)(mu), where the weight is a fundamental solution of this operator. It is shown that this property holds for mu as above while there is an interval [A(n), 1/2n - A(n)], where A(n) -->1, as n-->infinity, with mu-values for which the property does not hold. This interval is non-empty for ngreater than or equal to8.
|
|
| 21. |
- Forsgård, Jens, et al.
(författare)
-
On the order map for hypersurface coamoebas
- 2015
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 53:1, s. 79-104
-
Tidskriftsartikel (refereegranskat)abstract
- Given a hypersurface coamoeba of a Laurent polynomial f, it is an open problem to describe the structure of the set of connected components of its complement. In this paper we approach this problem by introducing the lopsided coamoeba. We show that the closed lopsided coamoeba comes naturally equipped with an order map, i.e. a map from the set of connected components of its complement to a translated lattice inside the zonotope of a Gale dual of the point configuration . Under a natural assumption, this map is a bijection. Finally we use this map to obtain new results concerning coamoebas of polynomials of small codimension.
|
|
| 22. |
- Frank, Rupert L.
(författare)
-
On the Laplacian in the halfspace with a periodic boundary condition
- 2006
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 44:2, s. 277-298
-
Tidskriftsartikel (refereegranskat)abstract
- We study spectral and scattering properties of the Laplacian H-(sigma)= - Delta in L-2 (R-+(d+1)) corresponding to the boundary condition (partial derivative u)/(partial derivative v) + partial derivative u = 0 with a periodic function sigma. For non-negative sigma we prove that H-(sigma) is unitarily equivalent to the Neumann Laplacian H-(0). In general, there appear additional channels of scattering due to surface states. We prove absolute continuity of the spectrum of H-(sigma) under mild assumptions on sigma.
|
|
| 23. |
- Götmark, Elin, 1979
(författare)
-
Weighted integral formulas on manifolds
- 2008
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 46:1, s. 43-68
-
Tidskriftsartikel (refereegranskat)abstract
- We present a method of finding weighted Koppelman formulas for $(p,q)$-forms on $n$-dimensional complex manifolds $X$ which admit a vector bundle of rank $n$ over $X \times X$, such that the diagonal of $X \times X$ has a defining section. We apply the method to $\Pn$ and find weighted Koppelman formulas for $(p,q)$-forms with values in a line bundle over $\Pn$. As an application, we look at the cohomology groups of $(p,q)$-forms over $\Pn$ with values in various line bundles, and find explicit solutions to the $\dbar$-equation in some of the trivial groups. We also look at cohomology groups of $(0,q)$-forms over $\Pn \times \Pm$ with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds.
|
|
| 24. |
|
|
| 25. |
- Hedenmalm, Håkan, 1961-
(författare)
-
Closed ideals in the bidisc algebra
- 1990
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 28, s. 111-117
-
Tidskriftsartikel (refereegranskat)
|
|
| 26. |
|
|
| 27. |
|
|
| 28. |
|
|
| 29. |
- Holst, Lars
(författare)
-
A note on records in a random sequence
- 2011
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 49:2, s. 351-356
-
Tidskriftsartikel (refereegranskat)abstract
- In an infinite sequence of independent identically distributed continuous random variables we study the number of strings of two subsequent records interrupted by a given number of non-records. By embedding in a marked Poisson process we prove that these counts are independent and Poisson distributed. Also the distribution of the number of uninterrupted strings of records is considered.
|
|
| 30. |
- Hultman, Axel
(författare)
-
The finite antichain property in Coxeter groups
- 2007
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 45:1, s. 61-69
-
Tidskriftsartikel (refereegranskat)abstract
- We prove that the weak order on an infinite Coxeter group contains infinite antichains if and only if the group is not affine.
|
|
| 31. |
- Hynd, Ryan, et al.
(författare)
-
Decay of extremals of Morrey’s inequality
- 2024
-
Ingår i: Arkiv för matematik. - : International Press, Inc.. - 0004-2080 .- 1871-2487. ; 62:1, s. 73-81
-
Tidskriftsartikel (refereegranskat)abstract
- We study the decay (at infinity) of extremals of Morrey’s inequality in Rn. These are functions satisfying (Formula Presented) where p>n and C(p, n) is the optimal constant in Morrey’s inequality. We prove that if n≥2 then any extremal has a power decay of order β for any (Formula Presented).
|
|
| 32. |
- Hytönen, Tuomas, et al.
(författare)
-
On the Carleson duality
- 2013
-
Ingår i: Arkiv for Matematik. - : International Press of Boston. - 1871-2487 .- 0004-2080. ; 51:2, s. 293-313
-
Tidskriftsartikel (refereegranskat)abstract
- As a tool for solving the Neumann problem for divergence form equations, Kenig and Pipher introduced the space X of functions on the half space, such that the non-tangential maximal function of their L_2-Whitney averages belongs to L_2 on the boundary. In this paper, answering questions which arose from recent studies of boundary value problems by Auscher and the second author, we find the pre-dual of X, and characterize the pointwise multipliers from X to L_2 on the half space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to L_p generalizations of the space X. Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.
|
|
| 33. |
- Hägg, Christian
(författare)
-
The asymptotic zero-counting measure of iterated derivaties of a class of meromorphic functions
- 2019
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 57:1, s. 107-120
-
Tidskriftsartikel (refereegranskat)abstract
- We give an explicit formula for the logarithmic potential of the asymptotic zero-counting measure of the sequence {(d(n)/dz(n)) (R(z) expT(z))}(n=1)(infinity). Here, R(z) is a rational function with at least two poles, all of which are distinct, and T(z) is a polynomial. This is an extension of a recent measure-theoretic refinement of Polya's Shire theorem for rational functions.
|
|
| 34. |
- Ivarsson, Björn
(författare)
-
On the behavior of strictly plurisubharmonic functions near real hypersurfaces
- 2007
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 45:1, s. 71-82
-
Tidskriftsartikel (refereegranskat)abstract
- We describe the behavior of certain strictly plurisubharmonic functions near some real hypersurfaces in ℂ n , n≥3. Given a hypersurface we study continuous plurisubharmonic functions which are zero on the hypersurface and have Monge–Ampère mass greater than one in a one-sided neighborhood of the hypersurface. If we can find complex curves which have sufficiently high contact order with the hypersurface then the plurisubharmonic functions we study cannot be globally Lipschitz in the one-sided neighborhood.
|
|
| 35. |
- Janson, Svante, 1955-
(författare)
-
A.s. convergence for infinite colour Pólya urns associated with random walks
- 2021
-
Ingår i: Arkiv för matematik. - : INT PRESS BOSTON, INC. - 0004-2080 .- 1871-2487. ; 59:1, s. 87-123
-
Tidskriftsartikel (refereegranskat)abstract
- We consider Polya urns with infinitely many colours that are of a random walk type, in two related versions. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on the offset distribution. This improves results by Bandyopadhyay and Thacker (2014-2017; convergence in probability), and Mailler and Marckert (2017; a.s. convergence assuming exponential moment).
|
|
| 36. |
- Janson, Svante, et al.
(författare)
-
Phase transitions for modified Erdős–Rényi processes
- 2012
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 50:2, s. 305-329
-
Tidskriftsartikel (refereegranskat)abstract
- A fundamental and very well studied region of the Erdős–Rényi process is the phase transition at m∼n/2 edges in which a giant component suddenly appears. We examine the process beginning with an initial graph. We further examine the Bohman–Frieze process in which edges between isolated vertices are more likely. While the positions of the phase transitions vary, the three processes belong, roughly speaking, to the same universality class. In particular, the growth of the giant component in the barely supercritical region is linear in all cases.
|
|
| 37. |
- Janson, Svante, et al.
(författare)
-
Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs
- 2011
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 49:1, s. 79-96
-
Tidskriftsartikel (refereegranskat)abstract
- General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph a"<, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.
|
|
| 38. |
- Johansson, Kurt
(författare)
-
A multi-dimensional Markov chain and the Meixner ensemble
- 2010
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 48:1, s. 79-95
-
Tidskriftsartikel (refereegranskat)abstract
- We show that the transition probability of the Markov chain (G(i,1),...,G(i,n)) (ia parts per thousand yen1), where the G(i,j)'s are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently been obtained by Warren in a Brownian motion model. Furthermore we demonstrate that this formula leads to the Meixner ensemble when we compute the distribution function for G(m,n). We also obtain the Fredholm determinant representation of this distribution, where the kernel has a double contour integral representation.
|
|
| 39. |
|
|
| 40. |
- Karlsson, A
(författare)
-
Boundaries and random walks on finitely generated infinite groups
- 2003
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 41:2, s. 295-306
-
Tidskriftsartikel (refereegranskat)abstract
- We prove that almost every path of a random walk oil a finitely generated nonamenable group converges in the compactification of the group introduced by W. J. Floyd. In fact, we consider the more general setting of ergodic cocycles of some semigroup of one-Lipschitz maps of a complete metric space with a boundary constructed following Gromov. We obtain in addition that when the Floyd boundary of a finitely generated group is non-trivial, then it is in fact maximal in the sense that it can be identified with the Poisson boundary of the group with reasonable measures. The proof relies on works of Kaimanovich together with visibility properties of Floyd boundaries. Furthermore, we discuss mean proximality of partial derivative Gamma and a conjecture of McMullen. Lastly, related statements about the convergence of certain sequences of points, for example quasigeodesic rays or orbits of one-Lipschitz maps, are obtained.
|
|
| 41. |
- Karlsson, Cecilia
(författare)
-
Area-preserving isotopies of self-transverse immersions of S (1) in a"e(2)
- 2013
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 51:1, s. 85-97
-
Tidskriftsartikel (refereegranskat)abstract
- Let C and C' be two smooth self-transverse immersions of S (1) into a"e(2). Both C and C' subdivide the plane into a number of disks and one unbounded component. An isotopy of the plane which takes C to C' induces a one-to-one correspondence between the disks of C and C'. An obvious necessary condition for there to exist an area-preserving isotopy of the plane taking C to C' is that there exists an isotopy for which the area of every disk of C equals that of the corresponding disk of C'. In this paper we show that this is also a sufficient condition.
|
|
| 42. |
- Kruglyak, Natan, et al.
(författare)
-
Sharp integral estimates for the fractional maximal function and interpolation
- 2006
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 44:2, s. 309-326
-
Tidskriftsartikel (refereegranskat)abstract
- We give sharp estimates for the fractional maximal function in terms of Hausdorff capacity. At the same time we identify the real interpolation spaces between L 1 and the Morrey space L 1,λ . The result can be viewed as an analogue of the Hardy-Littlewood maximal theorem for the fractional maximal function.
|
|
| 43. |
- Kruglyak, Natan, et al.
(författare)
-
The failure of the Hardy inequality and interpolation of intersections
- 1999
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 37:2, s. 323-244
-
Tidskriftsartikel (refereegranskat)abstract
- The main idea of this paper is to clarify why it is sometimes incorrect to interpolate inequalities in a “formal” way. For this we consider two Hardy type inequalities, which are true for each parameter α≠0 but which fail for the “critical” point α=0. This means that we cannot interpolate these inequalities between the noncritical points α=1 and α=−1 and conclude that it is also true at the critical point α=0. Why? An accurate analysis shows that this problem is connected with the investigation of the interpolation of intersections (N∩L p(w0), N∩Lp(w1)), whereN is the linear space which consists of all functions with the integral equal to 0. We calculate theK-functional for the couple (N∩L p(w0),N∩L p (w1)), which turns out to be essentially different from theK-functional for (L p(w0), Lp(w1)), even for the case whenN∩L p(wi) is dense inL p(wi) (i=0,1). This essential difference is the reason why the “naive” interpolation above gives an incorrect result.
|
|
| 44. |
- Kurasov, Pavel, 1964-
(författare)
-
Graph Laplacians and Topology
- 2008
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487.
-
Tidskriftsartikel (refereegranskat)
|
|
| 45. |
|
|
| 46. |
- Källström, Rolf, 1960-
(författare)
-
D-modules with finite support are semi-simple
- 2014
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 52:2, s. 291-299
-
Tidskriftsartikel (refereegranskat)abstract
- Let (R,m,k) be a regular local k-algebra satisfying the weak Jacobian criterion, and such that kR/k is an algebraic field extension. Let D be the ring of k-linear differential operators of R. We give an explicit decomposition of the DR-module D/Dm^(n+1) as a direct sum of simple modules, all isomorphic to D/Dm, where certain “Pochhammer” differential operators are used to describe generators of the simple components.
|
|
| 47. |
- Lagerberg, Aron, 1983
(författare)
-
A new generalization of the Lelong number
- 2013
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 51:1, s. 125-156
-
Tidskriftsartikel (refereegranskat)abstract
- We will introduce a quantity which measures the singularity of a plurisubharmonic function phi relative to another plurisubharmonic function psi, at a point a. We denote this quantity by nu (a,psi) (phi). It can be seen as a generalization of the classical Lelong number in a natural way: if psi=(n-1)log| a <...aEuro parts per thousand a'a|, where n is the dimension of the set where phi is defined, then nu (a,psi) (phi) coincides with the classical Lelong number of phi at the point a. The main theorem of this article says that the upper level sets of our generalized Lelong number, i.e. the sets of the form {z:nu (z,psi) (phi)a parts per thousand yenc} where c > 0, are in fact analytic sets, provided that the weight psi satisfies some additional conditions.
|
|
| 48. |
- Larson, Simon
(författare)
-
Maximizing Riesz means of anisotropic harmonic oscillators
- 2019
-
Ingår i: Arkiv för matematik. - : INT PRESS BOSTON, INC. - 0004-2080 .- 1871-2487. ; 57:1, s. 129-155
-
Tidskriftsartikel (refereegranskat)abstract
- We consider problems related to the asymptotic minimization of eigenvalues of anisotropic harmonic oscillators in the plane. In particular we study Riesz means of the eigenvalues and the trace of the corresponding heat kernels. The eigenvalue minimization problem can be reformulated as a lattice point problem where one wishes to maximize the number of points of (N-1/2) x (N-1/2) inside triangles with vertices (0, 0), (0, lambda root beta) and (lambda/root beta, 0) with respect to beta>0, for fixed lambda >= 0. This lattice point formulation of the problem naturally leads to a family of generalized problems where one instead considers the shifted lattice (N+sigma)x(N+tau), for sigma, tau>-1. We show that the nature of these problems are rather different depending on the shift parameters, and in particular that the problem corresponding to harmonic oscillators, sigma=tau=-1/2, is a critical case.
|
|
| 49. |
- Lenells, Jonatan, 1981-
(författare)
-
Riemannian geometry on the diffeomorphism group of the circle
- 2007
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 45:2, s. 297-325
-
Tidskriftsartikel (refereegranskat)abstract
- The topological group Dk(S) of diffeomorphisms of the unit circle S of Sobolev class H k , for k large enough, is a Banach manifold modeled on the Hilbert space Hk(S) . In this paper we show that the H 1 right-invariant metric obtained by right-translation of the H 1 inner product on TidDkbbS)\simeq Hk(S) defines a smooth Riemannian metric on Dk(S) , and we explicitly construct a compatible smooth affine connection. Once this framework has been established results from the general theory of affine connections on Banach manifolds can be applied to study the exponential map, geodesic flow, parallel translation, curvature etc. The diffeomorphism group of the circle provides the natural geometric setting for the Camassa-Holm equation - a nonlinear wave equation that has attracted much attention in recent years - and in this context it has been remarked in various papers how to construct a smooth Riemannian structure compatible with the H 1 right-invariant metric. We give a self-contained presentation that can serve as a detailed mathematical foundation for the future study of geometric aspects of the Camassa-Holm equation.
|
|
| 50. |
- Luger, Annemarie, et al.
(författare)
-
A characterization of Herglotz–Nevanlinna functions in two variables via integral representations
- 2017
-
Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 55:1, s. 199-216
-
Tidskriftsartikel (refereegranskat)abstract
- We derive an integral representation for Herglotz-Nevanlinna functions in two variables, which provides a complete characterization of this class in terms of a real number, two non-negative numbers and a positive measure satisfying certain conditions. Further properties of the class of representing measures are also discussed.
|
|
